A full descriptive definition of the Henstock-Kurzweil integral in the euclidean space

Proceedings of the London Mathematical Society

Volumn 87, Issue 3, 2003, Pages 677-700

  Lee, Tuo Yeong ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242408466     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611503014163     Document Type: Conference Paper

References (38)

1. B. BONGIORNO, 'Essential variation', Measure theory, Oberwolfach, 1981 (ed. D. Kölzow and D. Maharam-Stone), Lecture Notes in Mathematics 945 (Springer, Berlin, 1981) 187-193.
2. B. BONGIORNO, 'On the minimal solution of the problem of primitives', J. Math. Anal. Appl. 251 (2000) 479-487.
3. m,, J. Math. Anal. Appl. 224 (1998) 22-33.
4. B. BONGIORNO, L. Di PIAZZA and V. SKVORTSOV, 'The essential variation of a function and some convergence theorems', Anal. Math. 22 (1996) 3-12.
5. B. BONGIORNO, L. DI PIAZZA and V. SKVORTSOV, 'A new descriptive characterization of the Denjoy-Perron integral', Real Anal. Exchange 21 (1995/96) 656-663.
6. B. BONGIORNO, L. Di PIAZZA and V. SKVORTSOV, 'On continuous major and minor functions for the n-dimensional Perron integral', Real Anal. Exchange 22 (1996/97) 318-327.
7. B. BONGIORNO, L. DI PIAZZA and V. SKVORTSOV, 'On variational measures related to some bases', J. Math. Anal. Appl. 250 (2000) 533-547.
8. B. BONGIORNO, W. F. PFEFFER and B. S. THOMSON, 'A full descriptive definition of the gage integral', Canad. Math. Bull. 39 (1996) 390-401.
9. A. M. BRUCKNER, J. B. BRUCKNER and B. S. THOMSON, Real analysis (Prentice-Hall, Englewood Cliffs, NJ, 1997).
10. Z. BUCZOLICH, THIERRY DE PAUW and W. F. PFEFFER, 'Charges, BV functions, and multipliers for generalized Riemann integrals', Indiana Univ. Math J. 48 (1999) 1471-1511.
11. Z. BUCZOLICH and W. F. PFEFFER, 'Variations of additive functions', Czechoslovak Math J. 47 (1997) 525-555.
12. Z. BUCZOLICH and W. F. PFEFFER, 'On absolute continuity', J. Math. Anal. Appl. 222 (1998) 64-78.
13. m,, Czechoslovak Math. J. 51 (2001) 95-110.
14. CLAUDE-ALAIN FAURE, 'A descriptive definition of some multidimensional gauge integrals', Czechoslovak Math. J. 45 (1995) 549-562.
15. R. A. GORDON, The integrals of Lebesgue, Denjoy, Perron, and Henstock, Graduate Studies in Mathematics 4 (American Mathematical Society, Providence, RI, 1994).
16. J. JARNÍK and J. KURZWEIL, 'Perron-type integration on n-dimensional intervals and its properties', Czechoslovak Math. J. 45 (1995) 79-106.
17. W. B. JURKAT and R. W. KNIZIA, 'A characterization of multi-dimensional Perron integrals and the fundamental theorem', Canad. J. Math. 43 (1991) 526-539.
18. J. KURZWEIL and J. JARNÍC, 'Equi-integrability and controlled convergence of Perron-type integrable functions', Real Anal. Exchange 17 (1991/92) 110-139.
19. J. KURZWEIL and J. JARNÍK, 'Differentability and integrability in n dimensions with respect to α-regular integrals', Results Math 21 (1992) 138-151.
20. J. KURZWEIL and J. JARNÍC, 'Perron type integration on n-dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence', Czechoslovak Math. J. 46 (1996) 1-20.
21. LEE PENG YEE and CHEW TUAN SENG, 'Integration of highly oscillatory functions in the plane', Proceedings of the Asian Mathematical Conference, Hong Kong, 1990 (ed. Zhong Li, K. P. Shum, C. C. Yang and Le Yang, World Scientific, Singapore, 1992) 276-279.
22. LEE PENG YEE and NG WEE LENG, 'The Radon-Nikodym theorem for the Henstock integral in Euclidean space', Real Anal. Exchange 22 (1996/97) 677-687.
23. LEE PENG YEE and RUDOLF VYBORNY, The integral, an easy approach after Kurzweil and Henstock, Australian Mathematical Society Lecture Series 14 (Cambridge University Press, 2000).
24. LEE TUO YEONG, CHEW TUAN SENG and LEE PENG YEE, 'On Henstock integrability in Euclidean spaces', Real Anal. Exchange 22 (1996/97) 382-389.
25. LU JITAN and LEE PENG YEE, 'The primitives of Henstock integrable functions in Euclidean space', Bull. London Math. Soc. 31 (1999) 173-180.
26. J. MAWHIN, 'Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields', Czechoslovak Math. J. 31 (1981) 614-632.
27. PIOTR MIKUSIŃSKI and K. M. OSTASZEWSKI, 'The space of Henstock integrable functions II', New integrals (ed. P. S. Bullen, P. Y. Lee, J. L. Mawhin, P. Muldowney and W. F. Pfeffer), Lecture Notes in Mathematics 1419 (Springer, Berlin, 1990) 136-149.
28. K. M. OSTASZEWSKI, 'Henstock integration in the plane', Mem. Amer. Math. Soc. 353 (1986).
29. K. M. OSTASZEWSKI, 'The space of Henstock integrable functions of two variables', Internat. J. Math. Math. Sci. 11 (1988) 15-21.
30. W. F. PFEFFER, The Riemann approach to integration (Cambridge University Press, 1993).
31. W. F. PFEFFER, 'The generalized Riemann-Stieltjes integral', Real Anal Exchange 21 (1995/96) 521-547.
32. W. F. PFEFFER, 'On variations of functions of one real variable', Comment. Math. Univ. Carolin. 38 (1997) 61-71.
33. W. F. PFEFFER, 'The Lebesgue and Denjoy-Perron integrals from a descriptive point of view', Ricerche Mat. 48 (1999) 211-223.
34. W. F. PFEFFER and B. S. THOMSON, 'Measures defined by gages', Canad. J. Math. 44 (1992) 1303-1316.
35. S. SAKS, Theory of the integral, 2nd edn (Dover, New York, 1964).
36. B. S. THOMSON, 'Derivates of interval functions', Mem. Amer. Math. Soc. 452 (1991).
37. B. S. THOMSON, 'σ-finite Borel measures on the real line', Real Anal. Exchange 23 (1997/98) 185-192.
38. B. S. THOMSON, 'Some properties of variational measures', Real Anal. Exchange 24 (1998/99) A 845-853.